Chi Square Test and Contingency Table

15.2 During last year's budget crunch, several deserving employees of the Bureau of Procedures (BP) were denied promotions. This year, an unusual number of BP employees retired. The bureau chief suspects that the denial of promotions resulted in increased retirements. Of the 115 employees denied promotion, 32 retired. Of the 58 employees promoted, 9 retired. Present a contingency table, and analyze this information.

15.4 Auditors for the Military Airlift Command (MAC) are checking the arrival times of the three charter airlines they used in the Pacific last year. Branflake Airways flew 135 flights and was late 78 times. Flying Armadillo Airlines flew 94 flights and was late 35 times. Air Idaho flew 115 flights, with 51 late arrivals. Set up a contingency table, and analyze it for MAC.

16.4 Two scholars are locked in debate regarding the interpretation of the accompanying data. One insists that the relationship between the age of a child and the child's perception of the parents is very strong; the other argues that no relationship exists. Why do the two scholars reach different conclusions? Analyze the table and resolve the dilemma. Is there a relationship between the age of a child and the child's perception of the parents?
Age of Child (Years)
Child's Perception of Parents 5-15 16-27 28 and Older
Negative 11% 53% 23%
Neutral 18% 27% 59%
Positive 71% 20% 18%
Total 100% 100% 100%

16.6 The city parks commission has decided to redevelop a community park. Some members of the commission feel that refurbishment of existing park facilities is sufficient to meet the needs of the community; therefore, they advocate minimal redevelopment. Other members feel that such a small-scale project is pointless. They contend that improvement of the park will create greater public satisfaction with the park and thus will draw many more people than currently use it. An increase in patrons could exhaust existing facilities, thus necessitating further redevelopment. To resolve this disagreement, the commission hires a consultant to conduct a survey of community opinion. Among the questions asked are these: Do you regularly use the park? Do you consider park facilities satisfactory or unsatisfactory? From the cross-tabulation of these questions presented in the accompanying table, what should the consultant recommend to the commission?
Park Facilities
Use Park Unsatisfactory Satisfactory Total
No 401 107 508
Yes 180 50 230
Total 581 157 738
Total 100% 100% 100%

17.2 The Department of Defense is concerned about the number of Harrier crashes. The Air Force argues that the crashes result because many of these planes are piloted by marines. The data for this claim are shown in the following table:
Pilot
Result Marine Air Force Total
Crash 46 32 78
Did not crash 187 155 342
Total 233 187 420
When the number of flight hours of the pilot is controlled, the following pattern appears:
Pilot with Less Than 200 Hours Pilot with More Than 200 Hours
Result Marine Air Force Total Marine Air Force Total
Crash 36 26 62 10 6 16
Did not crash 62 51 113 125 104 229
Total 98 77 115 135 110 245
Analyze these tables and present your findings.

17.4 A researcher is conducting an experiment to determine support for the feminist movement. The experimental procedure consists of playing a tape recording of a meeting of a feminist organization for a group of subjects and then comparing their attitudes with those of a matched control group of subjects who are not exposed to the tape. At the conclusion of the experiment, the researcher is amazed to find that the tape recording apparently made no difference in attitude toward the feminist movement. Check this result in the following table:
Listened to Tape Recording
Attitude toward Feminist Movement
No Yes
Not favorable 40 39
Favorable 40 41
The researcher then decides to take into account the sex of the subjects and obtains the following tables:
MEN WOMEN
Listened to Tape Recording Listened to Tape Recording
Attitude toward Feminist Movement Attitude toward Feminist Movement ???? No Yes No Yes
Not favorable 21 24 Not favorable 19 15
Favorable 19 16 Favorable 21 25
Did the tape recording have an effect on attitude toward the feminist movement? Explain your answer.

Solution Summary

The solution gives detailed steps on conducting the chi square test to check the independent of two variables by setting up a contingency table.

Please help with the following problem.
Describe the chi-squaretest of independence.
Give an example of a question that could be answered using this test.
If you were to assemble a contingencytable, what would be included in your rows and columns?
Pick a cell of this contingencytableand explain what the value

A research organization has collected the following data on household size and telephone ownership for 200 U.S. households at the 0.05 level, are the two variables independent? Based on the chi-squaretable, what is the most accurate statement that can be made about the p-value for the test?

12. In a contingencytable, when all the expected frequencies equal the observed frequencies the calculated 2 statistic equals 1. FALSE
13. In a contingencytable, if all of the expected frequencies equal the observed frequencies, then we can conclude that there is a perfect dependence between rows and columns. TRUE
14.

Is there an alternative test to the chisquared test? What if my results give an expected frequency below 5, which stats book states that these should be treated with caution? Is there a more appropriate stat test which would be more accurate in working out the significance of the results?

1) What are three lessons you learned relative ANOVA and Nonparametric tests?
2. Application of A Nonparametric Test - Chi-SquareTest of Independence
Given the following contingencytable problem:
The use of cellular phones in automobile has increased in the last few years. Of concern to traffic experts, as well as manufa

I need to find out if the percentage distribution differs for smokers and non-smokers between men and women. Use Chi-square (level of significance .05) testand need a 2 by 2 contingencytable that looks like:
Smokers found
Yes No
Males 12

Recognize a contingencytable (cross-tabulation of frequencies).
Find degrees of freedom and use the chi-squaretable of critical values.
Perform a chi-squaretest for independence on a contingencytable.
Perform a goodness-of-fit (GOF) test for a uniform distribution.
Explain the GOF test for a Poisson distribution.
Use co